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32.
Therefore, the corresponding Fourier series is
4A 
1
1
1

 sin θ + sin 3θ + sin 5θ + sin 7θ + 
π 
3
5
7

In writing the Fourier series we may not be
able to consider infinite number of terms for
practical reasons. The question therefore, is
– how many terms to consider?

40.
Even and Odd Functions
(We are not talking about even or
odd numbers.)

41.
Even Functions
Mathematically speaking -
f ( − θ ) = f (θ )
The value of the
function would
be the same
when we walk
equal distances
along the X-axis
in opposite
directions.

42.
Odd Functions
Mathematically speaking -
f ( − θ ) = − f (θ )
The value of the
function would
change its sign
but with the
same magnitude
when we walk
equal distances
along the X-axis
in opposite
directions.

43.
Even functions can solely be represented
by cosine waves because, cosine waves
are even functions. A sum of even
functions is another even function.
5
0
5
10
0
θ
10